Space harmonic amplifiers



Oct. 1, 1957 E D 2,808,532

SPACE HARMONIC AMPLIFIERS Filed Oct. 26, 1951 2 Sheets-Sheet 1 s TREA M INVENTOR A5575? M. F/A'LD ATTORNEY Oct. 1, 1957 M HELDv SPACE HARMONIC AMPLiFIERS I 2 She etS-Sheet 2 Filed Oct. 26, 1951 INVENTOR A 5 75/? M. F/EL D v B x /2/ $2M 2 N mh V 1 my] Q w w i NW 2H5. RN mm w m w \m mm \m ms a w NM m M Q T v/%// I mm W u r \N v r J Wm 5-..: C a RN m ATTORNEY United States Patent M SPACE HARMQNEC AMPLEFIERS Lester M. Field, Palo Alto, Calif., assignor to The Board of Trustees of the Leland Stanford Junior University, Stanford University, Calif, 21 legal entity of California Application October 26, 1951, Serial No. 253,343

3 Claims. (Cl. 315-35) This invention relates to travelling wave tubes, and more particularly to improvements in tubes of the space harmonic type, wherein travelling waves are propagated along a structure having longitudinally periodic variations (for example a wave guide with spaced transverse fins or slots) which provide alternate regions of strong field and weak field and thereby produce wave components having relatively low phase velocities, suitable for interaction with an electron stream projected along the structure.

For useful interaction to take place between a travelling wave and an electron stream, the wave or one of its components must have a phase velocity substantially equal to the electron speed. This is commonly around to /5 the velocity of light, depending upon the magnitude f the electron accelerating voltage that can be used. The required low phase velocity may be obtained by slowing the propagation of the wave, as by means of a helix or other suitable retardation line. However, as tubes are designed for higher frequencies, the required helix becomes smaller and more difficult to construct to the required accuracy. Moreover, the size of the elec- 9 tron beam which can be used is limited by the helix diameter, and the problems of beam interception and heat dissipation become more acute as the frequency is raised.

Periodically loaded structures such as internally finned wave guides have also been used as retardation or waveslowing devices. These are subject to about the same kind of limitations as the helix, although to a lesser extent in some cases. They operate, like the helix, by actually reducing the velocity of wave propagation to a value consistent with the electron velocity.

Space harmonic tubes operate by virtue of the fact that a single-frequency wave travelling along a periodic structure must necessarily consist of a series of Fourier component waves, all of the same frequency and the same group velocity, but of progressively lower phase velocities and correspondingly shorter guide wavelengths. The electron stream is made to have a velocity corresponding to the phase velocity of one of these components, and exchanges energy with it in substantially the same manner as in any other travelling wave tube. All of the other components have phase velocities widely different from the electron velocity, and no net direct interaction takes place between them and the electrons. However, the relative amplitudes of the various components remain constant, being determined by the dimensions of the propagating structure; so all will increase or decrease proportionately as energy is absorbed from or given up to the electron stream by the synchronous component. Thus useful interaction can be effected without slowing the principal or fundamental wave to the electron velocity.

In previous tubes of the space harmonic type, the fins or slots or equivalent elements have been designed to resonate at or very near the frequency of operation, in order to provide suitably high field intensities in the wave guide for effective interaction between the travelling wave and the electron stream. Perhaps as many as a hundred 2,808,532 Patented Oct. 1, 1957 or more such elements must be made as nearly identical as possible, with identical spacings between them. Furthermore, the dimensions must be exact in accordance with the desired operating frequency and beam voltage. These strict requirements make the practical construction of a useful tube very difiicult, since each slot or fin must be individually cut or milled to a high degree of precision.

One of the principal objects of the present invention is to provide space harmonic travelling wave tubes utilizing transverse resonance of the wave guide, instead of resonance of a large number of periodic elements, to make the guide impedance high and thereby produce relatively high field intensities in the path of the electron beam.

A corollary object is to provide space harmonic tubes whose operation does not depend upon resonance of the periodic elements, so that the dimensions of said elements are not critical and close tolerances-are not required.

Another object is to provide space harmonic tubes capable of operation throughout wider frequency bands than prior space harmonic tubes.

A further object is to provide an improved type of space harmonic wave propagating structure assembled from two parts which can easily be machined separately to the required precision.

Another object is to provide an improved type of space harmonic tube in which certain design limitations, as to the relative depths and spacingsof the periodic elements, are avoided.

The invention will be described with reference to the accompanying drawings, wherein:

Figs. 1 and 2 are longitudinal and transverse sections respectively of a wave guide with periodic variations constituted by spaced internal conductive fins or slots.

Fig. 3 is a graph of frequency against reciprocal wavelength in the guide of the structure of Fig. 1, showing the fundamental and first space harmonic wave characteristics,

Fig. 4 is a longitudinal section of a space harmonic tube embodying the invention,

Fig. 5 is a cross section of the structure of Fig. 4,

Fig. 6 is a modification of the device of Fig. 4, and

Fig. 7 is a perspective view of a modified space harmonic wave propagating structure.

The wave guide 1 shown in' Figs. 1 and 2 is of hollow rectangular cross section, with a series of transverse corrugations defined by internally extending conductive members 3. This guide is intended to operate with the electric field vector perpendicular to its broad sides, as indicated by the arrow E. The depth of the members 3, and of the slots between them is designated by the letter s. The length of one period, i. e., the longitudinal distance between a point on one transverse element and the corresponding point on an adjacent element, is d.

Referring to Fig. 3, the ordinates are frequency (cycles per unit time) and the abscissae are reciprocal guide wavelength (cycles per unit distance). The slope of a line on this graph thus has the dimensions The line 5 also represents wave propagation along an open sided parallel plate guide, such as would be formed 7 if the sides of theguidelwere removed and the transverse elements 3 were omitted.

With the conductive side walls present, but without the periodic transverse elements, the structure is an ordinary hollow pipe wave guide, having the propagation characteristics indicated by the dash line 7 in Fig. 3. In this case there are two different velocities to be considered: The group velocity v which is the velocity at which energy is propagated along the guide, and the phasevelocity v with which a phase front moves along the guide. These are generally not equal in a wave guide because the waves are propagated by two concurrent series of oblique reflections, alternately from one side wall to the other.

The group velocity at any given frequency f, is the slope of the line 7 at that point, as shown by the tangent line 9. The phase velocity is the slope of a line drawn from the origin to the corresponding point on the curve, like the line 11. It is apparent that the group velocity is always less than 0, being Zero at where W is the late 'al width of the guide. This is the low-frequency cutoff frequency f and at that frequency the Width W is one half the free space wavelength. As the frequency is increased from this value, the group velocity increases, asymptotically approaching c. The phase velocity, on the other hand, is always greater than 0, being infinite at f and decreasing asymptotically toward 0 as the frequency is increased. Y

The effect of adding periodic corrugations like the transverse elements 3 is to change the propagation characteristics to those represented by the solid line curve 13. The lower frequency region is not greatly different, although the cutoff frequency may be lowered somewhat. As the frequency is increased from the cutoff value, the curve at first coincides approximately with that for the simple enclosed wave guide, then starts to bend over to the horizontal. This is caused by the slots or spaces between the elements 3 acting as cavities which introduce series loading along the guide. These cavities are quarterwave resonant at where s is the depth of the slots.

AS the r quency r v is approached, the group velocity approaches zero, and the guide wavelength A; decreases rapidly. At a frequency f, somewhat below the guide wavelength becomes equal to. 2d, and the spacing between corresponding transverse surfaces of the elements 3 is one half wavelength. Transmission along the guide ceases abruptly at f, owing to. destructive interference between the reflections from the elements 3. Thus the corrugated guide of Fig. l exhibits a high frequency cutofi at f, in the neighborhood of energy stored per unit volume in the-wave. guide. is in-Q versely proportional to the group velocity. Thus as the group velocity is made lower, more energy is stored per unit volume, and the field intensity is higher.

As can be seen in Fig. 3, the lowest phase velocity obtainable with the above described fundamental waveslowing type of operation is somewhat more than times the free space velocity 0. When periodic guides are designed for fundamental operation at very high frequencies and/or relatively low phase velocities, it is found that the slot dimensions become prohibitively small, and it is not practical to build the device. Operation under conditions beyond the useful range of such periodic structures as simple wave-slowing means can be obtained by resorting to space harmonic interaction. 7

The phenomenon of space harmonics results from the fact that the electric fields in a periodic structure like that of Fig. l are concentrated in the regions 15, between the opposed ends of the elements 3, and are of relatively low intensity in the regions16 where the upper and lower conductive surfaces are furthest apart. Suppose the fundamental wave in the guide to have a high phase velocity, so, that the guide wavelength extends over many of the elements .3, for example twenty. Then any particular phase front of the wave, such as one at which the electric field is at a maximum from the top toward the bottom of the guide, would move a distance 20d during each R. F. cycle. An electron moving synchronously with this phase trout (assuming it were possible to make an electron move that fast) would always be in a unidirectional electric field, from top to. bottom.

'Now consider an electron moving much more slowly, so. that it travels, only the distance d during the time the phase front travelsv 21d. Letthis electron be in one of the high intensity field regions 15 when the phase front is passing it, i. e. at the instant when the electric field is at a maximum from top to bottom. One half cycle later the electron is overtaken and passed by an oppositely directed phase front, with the electric field extending from bottom to. top of the guide. But at this time, the electron is in one of the low intensity regions 16, and is relatively slightly affected by the field. The first downwardly directed phase front is followed at a distance 2011', by a second similar one which overtakes the, electron just as it passes hro h nea ig n ensity r on 15..

Thus as the electron travels along the guide, it encounters a field which alternates between a high intensity maximum in one direction (top to bottom), and. a low intensity maximum in the other direction. This is equivalent to a net unidirectional field, with an alternating field superimposed on it. The unidirectional component is, as far as the electron is concerned, exactly like the unidirectional field in which it; would; be if it were moving at the phase velocity of the fundamental wave. In other words, there appears to be a wave travelling with a phase velocity equal to the electron velocity, ,5 the velocity of the fundamental. This is the first space harmonic. By similar reasoning, the existence of a series of further higher order space harmonics can be deduced. These are ordinarily not of as much practical interest as the first harmonic, because their fields are weaker.

From the foregoing discussion, it can be seen that the guide wavelength of the first space harmonic is 1 Mi -E V? (in.

Thus the reciprocal guide wavelength of the first space harmonic at any frequency is more than that of the fundamental at that frequency. This is represented in Fig. 3 by the solid line 19, which is exactly like the line 13 representing the fundamental wave propagation, but displaced from it along the abscissa by the distance The first space harmonic (as well as the other harmonies, not indicated in Fig. 3) exhibits the same high frequency cutoff at f, near as the fundamental. Space harmonic tubes can be designed to operate near the high frequency cutoff to provide high field intensities in the guide in the same manner as in tubes using the fundamental wave, since the group velocity is low in this region, resulting in high energy storage. However, space harmonics operation near the high frequency cutoff has the following disadvantages:

l. The energy storage relied upon to provide high field intensities is caused by resonance of the elements 3, which act as a series of nearly @iarter wave cavities spaced at nearly half guide wavelength intervals along the guide. For successful operation, these cavities and their spacings must be as nearly identical as possible.

2. The required dimensions of the periodic elements 3 are extremely critical as to frequency. It is to be noted that the slot depth s must be about one quarter of the free space wavelength, whereas the slot spacing d has to be about one half of the guide wavelength.

3. The lowest attainable phase velocity using the first space harmonic near high frequency cutoff is one third the fundamental phase velocity. If lower phase velocities are required, higher order harmonics must be used. These give much weaker fields, for a given power flow through the guide, and the guide length must be made correspondingly greater to secure a given total energy exchange between the wave and the electron beam.

The principle of the present invention is based on space harmonic operation near the low frequency cutoff, at

Unlike the fundamental wave at this frequency, which has substantially infinite phase velocity, the space harmonic phase velocity is very low. The group velocity, on the other hand, is the same for the space harmonic wave as it is for the fundamental, and this is also very low near the cutoff frequency f The low group velocity results from the oblique reflection paths of the wave components in the guide in the same way as takes place in an ordinary smooth unloaded guide; it is not substantially affected by the presence or absence of the transverse members 3. But since the energy stored per unit volume, for a given power flow, is inversely proportional to the group velocity, the field intensity may be made substantially as high as desired by designing the guide to be near its low frequency cutoff width at the operating wavelength.

Referring to Fig. 3, it is observed that the phase velocity of the first space harmonic near the low frequency cutoff is about times the free space velocity, and is not a function of s. Thus the slot depth s has substantially no effect upon either the phase velocity or the group velocity, and the slots need only be made deep enough to produce alternate 6 regions of strong field and weak field along the guide. Since the operation does not depend upon resonance of the slots, the slot depths are not critical and need not be exactly identical.

Figs. 4 and 5 show a space harmonic travelling wave amplifier tube embodying the present invention. An electron gun 21 of usual design is arranged at one end of the tube to project a stream of electrons along the axis of a wave guide 23 to a collector electrode 25. The interior of the wave guide 23 has periodic variations in cross section constituted by inwardly extending transverse members 27. The members 27 may be provided on only one of the interior surfaces, if desired, leaving the other surface smooth.

The internal width W of the wave guide is made substantially one half the free space wavelength of the lowest frequency at which the tube is to be operated. The longitudinal spacing d between the transverse members 27 is determined by the velocity with which the electrons are projected through the guide, which in turn depends upon the beam voltage, i. e. the difference in the D.-C. potentials applied to the wave guide 23 and the cathode in the electron gun 21. As a typical example, the electron velocity may be one-tenth the velocity of light. In this case the required spacing d would be about onetenth the free space wavelength of the energy to be amplified, or about one fifth the guide width W. The inward extent s of the members 27 (or the depth of the slots between them) is not critical, but may be about one half d, or less. 7

The wave guide, electron gun and collector are surrounded by an evacuated envelope 29 which may be made of glass' The Wave guide 23 may be supported within the envelope by spring clips 31 or other suitable means, and the electron gun and collector elements may be supported on lead-in conductors extending through the ends of the envelope.

A conductive rod 33 extends across the narrow dimension of the guide 23 near one end thereof, through a hole 35 in the upper wall, and into a protuberance 37 in the wall of the envelope. As shown in Fig. 5, the rod 33 is located to one side of the longitudinal axis of the guide 23 so as not to intercept the electron beam. An input wave guide 39, outside the envelope 29, is provided with an aperture 41 through which the protuberance 39 and the end of the rod 33 may enter. This end of the rod 33 acts as a probe for coupling the input guide to the end of the guide 23. A similar arrangement 33, 3'7 couples the other end of the 'guide 23 to an output wave guide 43.

The end of the guide 23 adjacent the electron gun 21 may be closed except for an aperture 45, to act as an accelerating electrode.

In the operation of the described tube, the wave guide 23 is maintained at a high D.-C. potential, perhaps several thousand volts, positive with respect to the cathode, by means of a suitable external source such as a battery, not shown. The collector electrode 25 is also made positive with respect to the cathode, and may be connected to the same supply source as the wave guide.

High frequency energy supplied to the input wave guide 39 is transferred by way of the rod 33 to the guide 23, where it sets up a wave travelling toward the output end. As previously described in reference to Fig. 1, this wave induces fields in the guide which are alternately of high and low intensity, owing to the action of the members 27, thereby producing aspace harmonic component of relatively low phase velocity. The electron velocity is adjusted, by adjustment of the accelerating voltage, to correspond with this phase velocity.

Although the electric field lines in the guide are generally perpendicular to the axis, they are curved due to fringing at the edges of the transverse members, as indicated approximately in Fig. 1. Thus the electric fields have longitudinal components except at points on the axis,

and it is through these components that energy may be exchanged between the field and the electrons, which are deflected off the axis by the transverse, .(i. e. vertical) field components. Alternatively, the periodic discontinuities may be arranged to make the electric fields principally longitudinal, as by having the opposed sets of fins otfset axially. In either case, the fields tend to form the electron stream into bunches travelling slightly faster than the phase velocity of the space harmonic wave, and this causes the wave to increase in amplitude as it travels, absorbing part of the kinetic energy of the electrons substantially as in any other travelling wave tube. The amplified wave energy is transferred by the conductor 33 to the output guide 43, and thence to utilization means not shown.

Fig. 6 shows a modified arrangement for coupling an input Wave guide 39 to the space harmonic guide 23. In this case a transformer is used, comprising a wave guide section 51 whose Wide dimension is the same as that of the guide 23, and whose narrow dimension tapers from a value approximately equal to the space between the ends of the members 27 to a value corresponding to-the narrow dimension of the wave guide 39'. The larger end of the section 51 engages a block 53 which is cut out to form a mitre corner 55 and a short wave guide section 57 which has the same cross sectional dimensions as the guide 39. The block 53 is provided with an aperture 59 for the entry of the electron beam, and functions as an accelerating electrode or anode. A similar arrangement may be used for coupling to an output guide.

The wave guide 23 in Figs. 4 and 6 may be fabricated by milling the required slots in two slabs of metal, which are then joined face to face to form the internally ribbed enclosed guide. This has the disadvantage that the joints must be made at points where the currents flowingon the internal surfaces are high; any imperfection will introduce large losses. Another, and in some respects preferable construction for the periodic guide is shown in Fig. 7. Here the guide is also made in separate halves, but the plane of division is at the center of the broad sides. 'To provide the required alternate regions of strong field and weak field, matching slots 61 are cut. out along the edges of the two parts. When the parts are joined, the opposed slots 61 define a series of holes 63 lying opposite each other in the broad sides of the guide. The fields inside the guide will be weak in the vicinity of the holes, and strong between the holes.

The holes 63 may be covered by sheets of metal on the outer surface of the guide, but this is not essential. Also it is not essential that the joint between the two parts be perfect, since no current flows across the plane of division in the normal operation of the device.

It will be appreciated that the amplifying tube as described may be operated as an oscillator, it being -well known in the art that a tube producing amplification is in general usable as an oscillator, provided there is sufli cient feedback, external or internal, between the output and the input portions of the tube.

Since many changes could be made in theabove construction and many apparently widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1. A space harmonic travelling wave tube including a hollow conductor wave guide of substantially rectangular cross section and transverse width W with a series of transverse slots of depth s in one of its walls spaced at substantially equal intervals d longitudinally of the guide,

the depth s of said slots being less than one half the spacing d, means for producing and directing an electron beam with a velocity v substantially along the longitudinal axis of said guide, means for applying high frequency electromagnetic wave energy to one end of said guide, and means for leading such energy away from the other end of said guide, said width W, spacing d, and electron velocity v being related substantially as follows:

l c 2W where c is the velocity of electromagnetic wave propagation in free space.

2. A space harmonic travelling wave tube including a hollow rectangular wave guide having a low frequency cutoff at approximately the free space wavelength of the waves with which the device is to operate, said wave guide varying periodically in cross section at substantially equal intervals d along its length, an electron gun at one end of said guide positioned to direct a stream of electrons substantially at a velocity v along the longitudinal axis of said guide, a collector electrode at the other end of said guide positioned to receive said electrons after their passage through the guide, means for applying high frequency electromagnetic wave energy at substantially the cut-oif frequency of said wave guide to the first mentioned end of said guide and means for conducting amplified wave energy away from said other end, said intervals d, free space wavelength A, and i elocity v being related as follows:

where c is the velocity of electromagnetic wave propagation in free space.

3., A space harmonic travelling wave amplifier including a hollow rectangular wave guide having one cross sectional dimension W constant throughout its length and the other cross sectional dimension variable periodically at intervals d along said length, the variations being small compared to said intervals, an electron gun and a collector electrode at opposite ends of said wave guide oriented to direct an electron beam substantially along the longitudinal axis of said guide at a velocity v, and means coupling input and output wave guides to the respective ends of said first mentioned guide, said constant dimension W, intervals d, and velocity v being related as follows:

i 2 W a i where c is the velocity of light.

References Cited in the file of this patent UNITED STATES PATENTS 2,367,295 Llewellyn Jan. 16, 1945 2,511,407 Kleen et a1 June 13, 1950 2,566,087 Lerbs Aug. 28, 1951 2,643,353 Dewey June 23, 1953 2,645,737 Field July 14, 1953 2,653,270 Kompfner Sept. 22, 1953 2,683,238 Millman July 6, 1954 2,687,777 Warnecke et al. Aug. 31, 1954 FOREIGN PATENTS 951,115 France Apr. 11, 1949 OTHER REFERENCES Article by Chu and Hansen, pp. 996-1008, Iour. of Applied Physics, November 1947.

Article by I. R. Pierce pp. 24-29, Physics Today. for November 1950. i 

